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3 years ago

What is the slope of the line given by the equation y-9=15(x-5) ?

Mathematics

1 answer:

Alexxx [7]3 years ago

7 0

The final equation after distributing is:

y = 15x - 66

The slope is 15

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At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel

Alexeev081 [22]

Use Law of Cooling:
$T(t) = (T_0 - T_A)e^{-kt} +T_A$
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
$42 = (80-20)e^{-3k} +20 \\ \\ e^{-3k} = \frac{22}{60}=\frac{11}{30} \\ \\ k = -\frac{1}{3} ln (\frac{11}{30})$

Substituting k back into cooling equation gives:
$T(t) = 60(\frac{11}{30})^{t/3} + 20$

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
$T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\ \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80$
Solve for x:
$x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80$
Sub back into original cooling equation, x = T(t)
$-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20$
Solve for t:
$60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3} = 60 \\ \\ (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\ \\ \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\ \\ \\ t = 4.959$

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM

8 0

3 years ago

Help please!!<br> Solve for X.

Mekhanik [1.2K]

9514 1404 393

Answer:

3) x = 9

4) x = 3

Step-by-step explanation:

3) The two short segments are indicated as having a sum equal to the long segment.

(x +2) +(-5 +x) = 15

2x = 18 . . . . . . . . . . . . add 3

x = 9 . . . . . . . . . divide by 2

(This makes the segments be 9+2 = 11 and -5+9 = 4, which total 15.)

4) Same deal.

3x +3 = 4x

3 = x . . . . . . . . subtract 3x

(This makes the segments be 3(3) = 9 and 4(3) = 12, where 9+3=12.)

6 0

2 years ago

The number of adults who attend a county fair (measured in hundreds of people) is represented by the function a(d)=−0.3d2+4d+9 ,

Lesechka [4]

Given is the function for number of adults who visit fair at day 'd' after its opening, a(d) = −0.3d² + 4d + 9.

Given is the function for number of children who visit fair at day 'd' after its opening, c(d) = −0.2d² + 5d + 11.

Any function f(d) to find excess of children more than adults can be written as follows :-

f(d) = c(d) - a(d).

⇒ f(d) = (−0.2d² + 5d + 11) - (−0.3d² + 4d + 9)

⇒ f(d) = -0.2d² + 0.3d² + 5d - 4d + 11 - 9

⇒ f(d) = 0.1d² + d + 2

6 0

2 years ago

Read 2 more answers

17. Evaluate a. 6! b. 8P5 c. 12C4

Andreyy89

The factorial ! just means we multiply by every natural number less that the value so
6! =6×5×4×3×2×1= 720

for permutations we use the formula n!/(n-r)!
so we have 8!/(8-5)!=8!/3!=8×7×6×5×4

for combinations s we have n!/(n-r)!r!
so we have 12!/(12-4)!4!=12!/8!4!=12×11×10×9/4×3×2=11×10×9/2=99×5

7 0

3 years ago

All of the points in which quadrant have negative x-coordinates and negative y-coordinates?

pentagon [3]

Quadrant 3 or III
hope this helped

3 0

3 years ago

Read 2 more answers